Feral Cats & Bird Extinctions on Islands
Mathematical Biology Modeling Group
School of Mathematical Sciences &
School of Biological Sciences
J. Fielder
Serge Bloch, New York Times
September 28, 2009
I am a poor mathematician…I remain
mathematically semiliterate…
...I have succeeded to some extant in
theoretical model building by collaborating
with mathematical theoreticians…My role
was to suggest problems to be addressed, to
combine my intuition with theirs, and to
lay out empirical evidence unknown to
them. They were my intellectual prosthesis
and I theirs.
~ E. O. Wilson ~
Naturalist, 1994, page 122
Jennie Summerall
National Portrait Gallery, Washington, D. C.
Oil on canvas
M. Hayes
Key Goals of Today’s Lab
• Show how math can help explain ecological
processes.
• Demonstrate how biologists and
mathematicians can collaborate to address
problems that neither group could address
on their own.
Overview of Today’s Lab
• Problem with feral cats on islands and a possible
solution
• What role can math play?
– A gentle intro to mathematical modeling in ecology and
its use in evaluating management strategies
~ Take a break ~
• Go to computer lab for a simulation of population
dynamics on islands
• Wrap up
The Problem with Feral Cats on Islands
• Kerguelen Islands
(Chapuis 1995)
– 5 domestic founder cats
– How many cats will there be in
25 years?
– Before you answer, let’s take a
closer look at the island…
glennmci.brinkster.net
en.wikipedia.org
http://www.chthonic.f9.co.uk/b3ta/underage.jpg
Port-aux-Français
Capital settlement of Kerguelen Island,
French Territory
• 60 winter inhabitants
• 5 founder cats?...
• up to 120 summer inhabitants • 25 years later…30,000 cats
Birds killed per year?
> 3 million per year!
en.wikipedia.org/wiki/Port-aux-Français
Control of Feral Cats
• Culling & trapping
are expensive
• Time-consuming
• Labor intensive
• Controversial
• Disease
www.wildliferesearchmanagement.com.au
NYTimes
Diseases
• Feline Immunodeficiency Virus
=FIV
• Feline Leukemia Virus
=FeLV
www.morgansplace.com
Feline
Leukemia
Virus (FeLV)
• Retrovirus
• Found worldwide
• Spread by coming in contact with saliva, urine,
feces, and nasal secretions
American Association of Feline Practitioners and Cornell Feline Health Center, 2006
FeLV Characteristics
• Impossible to accurately predict the life expectancy of a cat with FeLV
• Signs of the disease
•
•
•
•
•
•
Loss of appetite, weight loss
Poor coat condition
Enlarged lymph nodes, may lead to cancer
Persistent diarrhea and fever
Inflammation of the gums
Seizures, behavior changes, and neurological disorders
• Primary stage
• Concentrated in bloodstream
• Some individuals become immune
• Secondary stage
• Later stage, infection in bone marrow and tissues
• Point of no return
• Leads to state of immune deficiency and cancer
American Association of Feline Practitioners and Cornell Feline Health Center, 2006
Questions
• What would you like to know before you
introduce feline leukemia into the cat
population on an island?
http://www.petcareloop.com/images/twitter_question_mark.png?1255219975
Some of Our Questions
• How deadly is the virus? How fast does it
spread?
• Does introducing the disease actually do
what you want it to do?
• How long will it take for the bird
population to grow to recover?
Modeling in Biology
• A tool for understanding
– Population growth or decline
– Ecological systems and process
– What variables in a system are
important
– Transmission of disease
– Migration of a population
– Habitat utilization
Example: Modeling Northern
Spotted Owl Population Data
•
•
•
•
Lives in old-growth forests
1985-2003 19+ years of data
11,432 birds marked
32,054 capture events
• This is complex data!
• Cost > $30,000,000
• Analyzed data using a
collaborative workshop of
biologists, statisticians, &
mathematicians.
Types of Questions in Modeling
Cat –Bird Populations
1. What information do we need to build a
model? (what’s important? what’s not?)
2. What questions can the model answer?
(what can the model predict?)
3. What questions can’t be answered by the
model?
Modeling Populations—2 Approaches
Measuring Total population
– Counts of animals, bacteria, trees, cells
– Aided by sampling
– Can be challenging/impossible to get accurate
estimates
Changes in population
– Birth rates, death rates, infection rates,
migration
– Describe interaction between species
Describing Rates Mathematically
dB
 rB
dt
dB
B

 rB 1  
dt
 K
• Seem complicated
• Can be analyzed
numerically and
graphically
• Easier to align with
biological factors
Exponential Growth Model
Graph of Total Population
Equation of Total Population
N  N 0e
rt
Equation of Population Change
dN
 rN
dt
Logistic Growth Model
Graph of Total Population
Equation of Total Population
N
K
 K
  rt
1 
 1 e
 N0 
Equation of Population Change
dN
 N
 rN 1  
dt
 K
Cat-Bird Dynamics
Tweety-Batman to the rescue!
(along with differential equations)
Predator-Prey with Logistic Growth
Birds
dB
 B
 rB B1    C
dt
 K
Cats

dC
C 

 rC C 1 
dt
 B/ 
Try an Example
dB
 B
 rB B1    C
dt
 K

dC
C 

 rC C 1 
dt
 B/ 
Starting Values
Graph of (Cat, Bird) Trajectory
Birds
Cats
What happens if a cat disease is
introduced to the system?
Birds
dB
 B
 rB B1    C
dt
 K
Cats

C 
dC
  ??
 rC C 1 
dt
 B/ 
The S-I-R Disease Equations
dS / dt
dI / dt
dR / dt
Describes how the number of
susceptible, infected, and recovered
individuals changes with time
The State Diagram for FeLV
A modified S-I-R model
b
b
Immune
Z
1-
Susceptible
X
σ
Viremic
(very brief)

Develop
Symptoms
Y
m
m
Death
• X+Y+Z = total population
α
m
Differential equations for FeLV
To the Computer Lab!
Conclusion
• What is modeling in biology, and how can
it be used as a tool for understanding
ecological systems?
• Biological influences on a system that go
into building a model
– birth rate, death rate, disease, im/em-igration,
food supply, etc.
Wrapping it up
• Yahoo article and worksheet
www.flickr.com/photos/bostich/3048320868/